Which mode should i trust for lighting?
Material Preview
Material Preview uses one of the builtin generic HDRi maps to light the objects.
It is for preview purposes only and wont affect final scene lighting, nor will it be exported along with the model.
In this mode scene lights are ignored (optionally) for performance and workflow reasons. You can enable them in the Shading Popover.
Render Preview
Render preview uses your actual World Shader as background color instead and lighting.
Scene lights are also previewed closer to final result. They are still never exported to other applications though, so in external game engine or environments results will always differ.
You can switch the HDRi on/off for both preview modes.

Also see related How to use Default HDRIs in Renders?